Why denser areas are more productive

A key driver of productivity is ease of resource allocation. This column uses firm-level data for France to show that misallocation has a spatial dimension: resource allocation and the associated effect on productivity are related not only to firms’ characteristics, but also to the environment in which they operate. Denser commuting zones seem to offer a better match between employers and employees, leading to more productive firms.

Is it selection, or the sorting of talents (Behrens et al., 2014) that leads only the most productive firms to locate in denser areas? Or do agglomeration economies explain why firms located in less dense environments are less productive? Empirical evidence suggests that the main driver of differences in productivity is not selection (i.e. tougher competition inducing less productive firms to exit the market) but agglomeration economies (Combes et al., 2012). Usual suspects are the higher availability of services, better infrastructures, sharing of public goods, a denser labor market allowing better matching, and technology spillovers (Duranton & Puga2004). Using firm level data for France we confirm in a recent CEPII working paper (Fontagné and Santoni, 2016) that misallocation has a spatial dimension: resource allocation and the associated effect on productivity are related not only to firms’ characteristics but also to the environment in which they operate. Denser commuting zones seem to offer a better match between employers and employees.

A key driver of productivity is ease of resource allocation: in a perfectly competitive environment resources should flow freely from less to more productive firms, since those are most likely to survive in the market. However, there are several factors that can hamper this continuous flow of resources: recessions, labor and capital rigidity or adverse regulatory and competitive environments. The resulting resource misallocation implies that more efficient firms tend to be smaller than the optimal size while less efficient firms tend to be bigger than their optimum production scale.

The dispersion of revenue-based productivity (the product of physical productivity and the firm's output price) has been used as an indicator of the degree of resource misallocation at the sectoral level (Hsieh and Klenow, 2009). Alternatively, the gap between the marginal product value of each factor and its cost to the firm can be used as a metric of the degree of resource misallocation among firms within sectors. It measures the extent to which firms are not fully optimizing production (Petrin and Sivadasan, 2013).

Notwithstanding the distortions that are present in the economy as a whole such as labor market rigidities, firms in denser areas should be able to match with more productive and better paid workers. In relation to the difference between the wage and the value of the marginal product, a better matching should reduce the gap between the two at firm level. Using administrative data for the universe of legal units operating in the French manufacturing sector over the period 1993-2007, we show that this mechanism is at work: resource misallocation among firms within sectors is lower in denser French commuting zones.

Our evaluation of input allocation is performed using firm level balance sheet data to retrieve total factor productivity (TFP) estimations, from which we derive the marginal contribution of production inputs. Then, using firm (or industry) specific input prices it is possible to derive a monetary value for the firm level allocation inefficiencies. We use balance sheet data comprising information on the location of the establishment considered at the commuting zone level (‘Zone d'emploi’): 340 commuting zones were defined jointly by the National Institute of Statistics (INSEE) and the French Ministry of Labor for statistical purposes and were revised in 2011 based on the 2006 census[1].

We illustrate this stylized fact by plotting in Figure 1 the density of firms' TFP for two firm categories in 2000 (in the middle of our time window), in commuting zones below and above the median urbanization: the premium is 6.5% significant at the 1% level.

For a given sector and year we report in Table 1 the mean absolute labor gap, defined as the distance from the social optimum allocation, where each firm is operating with marginal revenue equal to marginal costs and no frictions in the input markets. For the whole manufacturing sector over the period 1994-2007 this figure is slightly above 8,700 euro per firm at 2005 prices, with dispersion relatively high both between and also within industries, as shown by the coefficient of variation (CV). Instead of using perfect competition (zero gap) as the benchmark we are interested in knowing what the contribution to overall gains would be from achieving efficient allocation, i.e. the existing gaps are equal across all firms in a given sector. This results from the loosening of market constraints which allows the reallocation of one unit of labor (i.e. the marginal worker) across firms without changing the employment level or the structural frictions. This information is shown in column 4 (‘Contri’). For instance, in the case of machinery and equipment, resource allocation inefficiencies determine 50.2% of the mean absolute gap while structural frictions account for the other half of the overall gap.

Table 1: Average absolute labor gap by sector (years 1994-2007)

Mean

Gap > 0

CV

Contri

Obs

(Euro)

(%)

(%)

Basic metals

9,052

19.4

0.994

38.3

8,557

Beverages

18,488

66

1.095

33.8

9,836

Chemicals

12,572

36.8

1.155

96.1

20,788

Computer and Elect

14,123

12.2

0.776

23.6

25,965

Electrical Equip

10,449

13.1

0.837

29.9

17,229

Fabricated metal

8,226

17.8

0.894

38.1

145,354

Food products

6,644

27.7

1.093

62.4

133,132

Furniture

8,944

11.1

0.753

22.9

29,987

Leather products

7,056

28.2

1.32

76.7

8,937

Machinery and Equipment

9,794

21

0.968

50.6

53,899

Motor vehicles

8,727

19.9

1.088

52.2

14,335

Non-metallic pro

9,525

20.5

0.998

57.8

33,452

Other Manuf

9,897

23.8

0.97

59.9

37,700

Other transport

8,656

25.8

1.115

56.9

6,206

Paper products

8,747

25

1.028

59.4

15,449

Pharmaceutical

19,022

21.9

0.897

63.4

4,300

Printing and rec

9,142

17.3

0.954

36.4

66,649

Repair and instal

8,031

20.8

1.025

49.1

74,799

Rubber and plastic

8,306

23.7

1.003

56.6

38,555

Textiles

8,815

22.8

1.14

60.9

26,441

Wearing apparel

9,648

29.8

1.196

85.0

33,714

Wood products

6,457

22.8

1.033

48.7

37,475

Source: authors' calculations.

We finally investigate whether firms in denser areas exhibit lower labor gaps, controlling for firm productivity and export status. To do so, we focus on the matching channel efficiency, and test whether in denser areas the thicker labor market also favors firm resource allocation efficiency, reducing the return to cost wedge. We follow Martin et al. (2011) and define two indicators for each single-plant firm located in a given commuting zone and operating in a given sector: ‘Urbanization’ is the number of employees in other industries within the same commuting zone, and ‘Location’, is the number of employees working in the same industry and the same commuting zone. However, we should be aware that that the typical worker in denser areas is more skilled. Worker sorting by skills across cities would thus induce attenuation bias in any OLS estimation.

Our instrumental variable approach confirms the role of agglomeration: a 10 percent increase in the degree of urbanization is associated with a decrease in the average gap of about 240 euro (out of a mean gap of 9,680 euro). Instead, location has no impact: intra-industry externalities do not induce firm level efficiency.